Postdoc at MSU with Gideon Bradburd
PhD with Scott Nuismer at UI (def June 2020)
developed phenotypic models of coevolution
methods to measure coevolution from trait data
studied diffusion limits of eco-evo models
The reciprocal evolutionary response of two species to a shared ecological interaction
When this process plays out in spatially structured populations, characteristic patterns can emerge
Simple models predict bivariate distribution of traits
Can use maximum likelihood to infer strength of coevolution (Week & Nuismer 2019)
Caveat: spatially implicit
Ignores isolation by distance (IBD)
Which can confound inference
Accounting for IBD may increase power to detect coevolution
Courtesy Powell & Prior (2016)
How do the spatial scales at which phenotypic patterns emerge depend on:
dispersal distances?
coevolutionary selection?
How do spatial scales of local adaptation relate to spatial scales of phenotypic patterns?
How can we use this information to identify loci involved in coevolution?
Develop continuous space phenotypic model accounting for:
limited dispersal
random genetic drift
spatially homogeneous abiotic stabilizing selection
biotic coevolutionary selection
Ecologically important interaction
Genetics are relatively well understood
Evidence for gene-for-gene mechanisms mediating Linum marginale & Melampsora lini coevolution (Dodds et al 2006)
Evidence for balancing selection Daphnia magna & Pasteuria ramosa (Bento et al 2017, Andras et al 2020)
Has motivated studies in local adaptation
\(H=\) host, \(P=\) parasite
Fitness \(m_H,m_P\) determined by traits \(z_H,z_P\)
Selection: \(\mathrm{Cov}(m_H,z_H), \ \mathrm{Cov}(m_P,z_P)\)
Mean trait dynamics given by
\(\frac{d}{dt}\bar z_H=\mathrm{Cov}(m_H,z_H)+\delta_H \\ \frac{d}{dt}\bar z_P=\mathrm{Cov}(m_P,z_P)+\delta_P\)
\(\delta_H,\delta_P\) are stochastic processes representing drift
\(\mathrm{Cov}(m,z)=G\beta\)
\(G_H,G_P=\) additive genetic variances
\(\beta_H,\beta_P=\) selection gradients
\(\beta_H = -B_H(\bar z_P-\bar z_H) \\ \beta_P = \ B_P(\bar z_H-\bar z_P)\)
\(B_H,B_P=\) strengths of coevolutionary selection
2D space (\(x_1,x_2\))-coordinates
Assume offspring normally distributed around parents
\(\frac{\partial\bar z_S}{\partial t}=\color{red}{G_S\beta_S}+\color{blue}{\frac{\sigma_S^2}{2}\left(\frac{\partial^2\bar z_S}{\partial x_1^2}+\frac{\partial^2\bar z_S}{\partial x_2^2}\right)}+\color{green}{\delta_S} \\ S=H,P\)
\(\sigma_H,\sigma_P\propto\) expected dispersal distances
Need to add abiotic stabilizing selection to prevent runaway coevolution
\(\beta_H = \color{green}{A_H(\theta_H-\bar z_H)}-\color{blue}{B_H(\bar z_P-\bar z_H)} \\ \beta_P = \color{green}{A_P(\theta_P-\bar z_P)}+\color{blue}{B_P(\bar z_H-\bar z_P)}\)
\(A_H,A_P=\) strengths of abiotic stabilizing selection
\(\theta_H,\theta_P=\) abiotic optimal trait values
Assumes:
weak coevolutionary selection (\(B_H,B_P\ll1\)),
spatially homogeneous selection strengths
spatially homogeneous abiotic environment
traits encoded by many additive small effect loci
constant population densities in space and time
constant additive genetic variances